A new algorithm of non-Gaussian component analysis with radial kernel functions

Motoaki Kawanabe, Masashi Sugiyama, Gilles Blanchard, Klaus Muller

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit. The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions (IMAK), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples.

Original languageEnglish
Pages (from-to)57-75
Number of pages19
JournalAnnals of the Institute of Statistical Mathematics
Volume59
Issue number1
DOIs
Publication statusPublished - 2007 Mar 1
Externally publishedYes

Fingerprint

Kernel Function
Radial Functions
Projection Pursuit
Algorithm Analysis
Gaussian Noise
High-dimensional Data
Iterative Algorithm
Subspace
Tend
Metric
Numerical Examples
Alternatives

Keywords

  • Linear dimension reduction
  • Non-Gaussian subspace
  • Projection pursuit
  • Semiparametric model
  • Stein's identity

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

A new algorithm of non-Gaussian component analysis with radial kernel functions. / Kawanabe, Motoaki; Sugiyama, Masashi; Blanchard, Gilles; Muller, Klaus.

In: Annals of the Institute of Statistical Mathematics, Vol. 59, No. 1, 01.03.2007, p. 57-75.

Research output: Contribution to journalArticle

Kawanabe, Motoaki ; Sugiyama, Masashi ; Blanchard, Gilles ; Muller, Klaus. / A new algorithm of non-Gaussian component analysis with radial kernel functions. In: Annals of the Institute of Statistical Mathematics. 2007 ; Vol. 59, No. 1. pp. 57-75.
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